We're destroying the earth and suffocating in our own waste, yet "there's a good chance of productivity explosion by 2100 which could quickly lead to what one might call a "technologically mature" civilization"
It is possible for destruction to happen just fast enough for everybody to finally take notice, but not fast enough to preclude geoengineering solutions for good. That's one possible (if not pretty) path to get to a technologically mature stage.
The risk is always that we wake up already in a boiling frog state, or that even when dangers become self-evident for everybody, we still spend time on power games instead of fixing the problems. In that case, well, we kinda deserve it...
Sure there might be some life that survives the climate crisis after we're gone, but the planet is going to lose most of its biodiversity before then.
To be clear: Global warming is bad. It is going to kill tens of millions of people, drown a lot of cities, and render alarmingly large sections of the planet uninhabitable to unmodified humans.
It does not actually pose an existential threat to technological civilization. Even 5C of warming would not kill all humans.
The cities will just move north. We are not in danger of running out of oil or coal before transitioning to clean electricity. 2100 will look very different, (less international trade, almost certainly no unified global internet like we have now) but regular ole global capitalism will keep rolling along.
Humanity is not dealing with global warming very effectively. But it won't kill 100% of all humans. It won't even kill 50%.
You're greatly underestimating the societal impact that this will have. Cities don't 'just move' somewhere else in a few decades without causing massive turmoil. For one thing, the countries up north (or south) will not just accept (or be able to handle) a few hundred million immigrants. There will be global war, and it's hard to say what will be left at the end. At the very least, billions will die, not 'tens of millions'.
Not to mention, we have no idea what impact this will have on global agriculture. Like it or not, we are not entirely separated from existing ecosystems, and the destruction of most land-dwelling animals living near the equator will not be a small thing.